What is the answer to (1/4)^x+(1/2)^x-6=0 ?

The answer to (1/4)^x+(1/2)^x-6=0 is x=-1

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(1/4)^x+(1/2)^x-6=0

(\frac{1}{4})^{x} + (\frac{1}{2})^{x} - 6 = 0

x = - 1

Solution steps

(\frac{1}{4})^{x} + (\frac{1}{2})^{x} - 6 = 0

Apply exponent rules

((\frac{1}{2})^{x})^{2} + (\frac{1}{2})^{x} - 6 = 0

Rewrite the equation with

(\frac{1}{2})^{x} = u

(u)^{2} + u - 6 = 0

Solve

u^{2} + u - 6 = 0 : u = 2, u = - 3

u = 2, u = - 3

Substitute back

u = (\frac{1}{2})^{x},

solve for

x

Solve

(\frac{1}{2})^{x} = 2 : x = - 1

Solve

(\frac{1}{2})^{x} = - 3 :

No Solution for

x \in R

x = - 1

8 \cdot 3^{n - 1} - 21 = 51

3^{2 x} - 10 \times 3^{x} + 21 = 0

3^{2 x - 4} = 3^{5 x + 8}

y, x = 1 2^{1 - 0.1 y}

9 9^{x + 9} = 999 9^{x + 9}

What is the answer to (1/4)^x+(1/2)^x-6=0 ?
The answer to (1/4)^x+(1/2)^x-6=0 is x=-1
Solve for x: (1/4)^x+(1/2)^x-6=0
The solution is x=-1